Introduction
The global warming potential (GWP) is the primary metric used to assess the
equivalency of emissions of different greenhouse gases (GHGs) for use in
multi-gas policies and aggregate inventories. This primacy was established
soon after its development in 1990 (Lashof and Ahuja, 1990; Rodhe, 1990) due
to its early use by the WMO (1992) and UNFCCC (1995). However, despite the
GWP's long history of political acceptance, the GWP has also been a source of
controversy and criticism (e.g., Wigley et al., 1998; Shine et al., 2005;
Allen et al., 2016; Edwards et al., 2016).
Key criticisms of the metric are wide ranging. Criticisms include the
following: that radiative forcing as a measure of impact is not as relevant
as temperature or damages (Shine et al., 2005); that the assumption of
constant future GHG concentrations (Wuebbles et al., 1995; Reisinger et al.,
2011) is unrealistic; that discounting is preferred to a constant time period
of integration (Schmalensee, 1993); disagreements about the choice of time
horizon in the absence of discounting (Ocko et al., 2017); that dynamic
approaches would lead to a more optimal resource allocation over
time (e.g., Manne and Richels, 2001, 2006); that the
GWP does not account for non-climatic effects such as carbon fertilization or
ozone produced by methane (Shindell, 2015); and that pulses of emissions are
less relevant than streams of emissions (Alvarez et al., 2012).
Unfortunately, including these complicating factors would make the metric
less simple and transparent and would require reaching a consensus regarding
appropriate parameter values, model choices, and other methodology issues.
The simplicity of the calculation of the GWP is one of the reasons that the
use of the metric is so widespread.
In this paper, we focus on the choice of time horizon in the GWP as a key
choice that can reflect decision-maker values, but for which additional clarity
regarding the implications of the time horizon could be useful. We also
investigate the extent to which the choice of time horizon can incorporate
many of the complexities of assessing the impacts described in the previous
paragraph. The 100-year time horizon of the GWP (GWP100) is the time
horizon most commonly used in many venues, for example in trading regimes
such as under the Kyoto Protocol, perhaps in part because it was the middle
value of the three time horizons (20, 100, and 500 years) analyzed in the
IPCC First Assessment Report. However, the 100-year time horizon has been
described by some as arbitrary (Rodhe, 1990). The IPCC AR5 (Myhre et al.,
2013) stated that “[t]here is no scientific argument for selecting 100 years
compared with other choices”. The WMO (1992) assessment has provided one of
the few justifications for the 100-year time horizon, stating that “the GWPs
evaluated over the 100-year period appear generally to provide a balanced
representation of the various time horizons for climate response”. Recently,
some researchers and NGOs have been promoting more emphasis on shorter time
horizons, such as 20 years, which would highlight the role of short-lived
climate forcers such as CH4 (Howarth et al., 2011; Edwards and
Trancik, 2014; Ocko et al., 2017; Shindell et al., 2017). These studies each
have different nuances regarding their recommendations – for example, Ocko
et al. (2017) suggest pairing the GWP100 with the GWP20 to reflect both
long-term and near-term climate impacts – and therefore there is no simple
summary of the policy implications of this body of literature, but it is
plausible that more consideration of short-term metrics would result in
policy that weights near-term impacts more heavily. In contrast, some
governments have suggested the use of the 100-year global temperature change
potential (GTP) based on the greater physical relevance of temperature in
comparison to forcing, in effect downplaying the role of the same short-lived
climate forcers (Chang-Ke et al., 2013; Brazil INDC, 2015). Therefore, the
question of timescale remains unsettled and an area of active debate. We
argue that more focus on quantitative justifications for timescales within
the GWP structure would be of value, as differentiated from qualitative
justifications such as a need for urgency to avoid tipping points as
in Howarth et al. (2012).
While we argue that quantitative justifications for choosing appropriate GWP
timescales are rare, as reflected by the judgment of the IPCC authors that no
scientific arguments exist for selecting given timescales, there is a rich
literature addressing many aspects of climate metrics. Deuber et al. (2013)
present a conceptual framework for evaluating climate metrics, laying out
the different choices involved in choosing the measure of impact of radiative
forcing, temperature, or damages, and temporal weighting functions that can
be integrative (whether discounted or time horizon based) or based on single
future time points. Deuber et al. (2013) conclude that the global damage potential
(GDP) could be considered a “first-best benchmark metric”, but recognize
that the time-horizon-based GWP has advantages based on limiting value-based
judgments to a choice of time horizon, reducing scientific uncertainty by
limiting the calculations of atmospheric effects to radiative forcing, and
eliminating scenario uncertainty by assuming constant background
concentrations. Mallapragada and Mignone (2017) present a similar framework
and also note that metrics can consider a single pulse of a stream of pulses
over multiple years. Several authors have recognized that under certain
simplifying assumptions, the GWP is equivalent to the integrated GTP, and
therefore any timescale arguments that apply to analyses of one metric would
also apply to the other (Shine et al., 2005; Sarofim, 2012).
A few papers have applied GDP-type approaches to evaluate the GWP in a manner
similar to that of this paper. Boucher (2012) uses an uncertainty analysis
similar to that used in this paper to estimate the GDP of methane. Boucher
found that the GDP was highly sensitive to discount rate over a range of
1 % to 3 % and damage function over a range of polynomial exponents
of 1.5 to 2.5 and that the median value of the GDP was very similar to the
GWP100. Fuglestvedt et al. (2003) also used a GDP approach to map time
horizons and damage function exponents to a discount rate using IS92a as an
emission scenario. Fuglestvedt et al. (2003) found that a discount rate of
1.75 % and a damage exponent of 2 led to results equivalent to a GWP100.
De Cara (2005), in an unpublished manuscript, also calculated the
relationship between discount rates and time horizon, though they assumed
linear damages.
An alternate approach is to evaluate metrics within the context of an
integrated assessment model (IAM). There are several examples of such an
approach. Van den Berg et al. (2015) analyze the implications of the use of
20-, 100-, and 500-year GWPs for CH4 and N2O
reductions over time within an IAM. The analysis estimated optimal costs to
meet a 3.5 W m-2 target in 2100 and found that use of the GWP20
and GWP100 resulted in similar costs (within 4 %), but that use of
the GWP500 resulted in higher costs by 18 %. A key caveat here, as
with many such analyses (including the present Sarofim and Giordano paper),
is that the structure of the test can drive the evaluation result: in the
case of van den Berg et al. (2015), the analysis ends in 2100, which will
reduce the evaluated benefits of long-term metrics, particularly for
reductions that occur at the end of the century. These IAMs often use a
discount rate of 5 % for their net present value analysis. Other IAM
analyses have concluded that changing the CH4 to CO2
ratio away from the GWP100
has small effects on policy costs and climate outcomes (e.g., Smith et al.,
2013; Reisinger et al., 2013). This is in large part because marginal
abatement curves for CH4 within these models have low-cost options
(likely representing mitigation options such as landfill gas to energy
projects and oil and gas leakage reduction) and high-cost options (reductions
of enteric fermentation emissions from livestock) but few moderate-cost
options. Therefore, for even a moderate carbon price, all the low-cost
options will be enacted regardless of GWP, and no matter what the GWP, few
high-cost options will be enacted. Such analyses may not fully consider
non-market barriers or distributional effects for which changes in the GWP
could be important.
While this paper focuses on a cost–benefit approach, there is also a
potential need for cost–efficiency approaches, particularly in regard to
stabilization targets such as 2 ∘C. However, a number of authors
have argued that pulse-based metrics such as the GWP are not well-suited to
achieve stabilization goals (Sarofim et al., 2005; Smith et al., 2012; Allen
et al., 2016). Some actors (Brazil INDC, 2015) have claimed that certain
metrics such as the global temperature potential (Shine et al., 2005) or the
climate tipping potential (Jorgensen et al., 2014) are more compatible with a
stabilization target such as 2 ∘C because they are temperature
based. However, any pulse-based approach faces at least two major challenges
related to stabilization scenarios. The first is that as a temperature target
is approached, a dynamic approach will shift from favoring long-lived gas
mitigation to favoring short-lived gases. While this shift may be optimal for
meeting a target in a single year, it will be suboptimal for any year after
that year. The second challenge is that once stabilization has been achieved,
any trading between emission pulses of carbon dioxide and a shorter-lived gas
will cause a deviation from stabilization. For example, trading a reduction
in methane emissions for a pulse of CO2 emissions will lead to a
near-term decrease in temperature, but also a long-term increase in
temperature above the original stabilization level. One solution to the
problem is a physically based one. Allen et al. (2016) suggest trading an
emission pulse of carbon dioxide against a sustained change in the emissions
of a short-lived climate forcer. This resolves the issue of trading off what
is effectively a permanent temperature change against a transient one.
However, the challenge becomes one of implementation, as current policy
structures are not designed for addressing indefinite sustained mitigation. A
second solution is a dynamically updating global cost potential approach that
optimizes shadow prices of different gases given a stabilization constraint
(Tol et al., 2012), but again, implementation would be challenging.
Alternatively, a number of researchers (Daniel et al., 2012; Jackson, 2009;
Smith et al., 2012) suggest addressing CO2 mitigation separately
from short-lived gases. Such a separation recognizes the value of the
cumulative carbon concept in setting GHG mitigation policy (Zickfeld et al.,
2009). However, this approach requires a central decision-maker and loses the
“what” flexibility that makes the use of metrics appealing (Bohringer et
al., 2006). In economic terms, a temperature-based target is equivalent to
the assumption of infinite damage beyond that threshold temperature and zero
damages below that threshold (Tol et al., 2016).
This paper provides a needed quantification and analysis of the implications
of different GWP time horizons. We follow the lead of economists who have
proposed that the appropriate comparison for different options for GHG
emissions policies is between the net present discounted marginal
damages (Schmalensee, 1993; Deuber et al., 2013). However, instead of
proposing a switch to a GDP metric, we take the structure of the GWP as a
given due to the simplicity of calculation and the widespread historic
acceptance of its use. While other analysts have used similar approaches
(Fuglestvedt et al., 2003; Boucher, 2012), this paper reframes and clarifies
key issues and presents a framework for better understanding how different
timescales can be reconciled with how the future is valued. The paper focuses
on CO2 and CH4 as the two most important historical
anthropogenic contributors to current warming, but the methodology is
applicable to emissions of other gases, and sensitivity analyses consider
N2O and some fluorinated gases.
Methods
The general approach taken in this paper is to calculate
the impact of a pulse of emissions of either CO2 or CH4
in the first year of simulation on a series of climatic variables. The first
step is to calculate the perturbation of atmospheric concentrations over a
baseline scenario. The concentration perturbation is transformed into a
change in the global radiative forcing balance. The radiative forcing
perturbation over time is used to calculate the impact on temperature and
then damages due to that temperature change. Discount rates are then applied
to these impacts to determine the net present value of the impacts. The
details of these calculations are described here.
Concentrations. The perturbation due to a pulse of CO2 is
determined by the use of IPCC AR5 equations (see Table 8.SM.10 from the IPCC
AR5 assessment). The perturbation due to a pulse of CH4 is
calculated by the use of a 12.4-year lifetime, consistent with Table 8.A.1
from IPCC AR5. In this paper, a pulse of 28.3 Mt of CH4 is used
(sufficient for a 10 ppb change in global CH4 concentrations in
the pulse year; results of a larger pulse are described in Sect. 3.3). The
mass of the gas is converted to concentrations by assuming a molecular weight
of air of 29 g mole-1 and a mass of the atmosphere of 5.13×1018 kg. These perturbations are added to baseline concentration
pathways; for this study, we use the four RCP scenarios based on data from
http://www.pik-potsdam.de/~mmalte/rcps/ (last access: 14 August 2018).
This approach parallels the standard IPCC approach; however, various papers
have noted that the lifetime of CO2 presented in the IPCC includes
climate carbon feedbacks, whereas the lifetime of CH4 does not,
which is a potential inconsistency (Gasser et al., 2017; Sterner and
Johansson, 2017). The discussion in Sect. 3.3 and 3.4 elaborates on the
consequences of these choices.
Radiative forcing. The perturbation of radiative forcing from
additional GHG concentrations is based on the equations in Table 8.SM.1 from
IPCC AR5. CH4 forcing is adjusted by a factor of 1.65 to account
for effects on tropospheric ozone and stratospheric water vapor, as is
standard in GWP calculations. N2O forcing is adjusted by a factor of
0.928 to account for N2O impacts on CH4 concentrations, as
is also standard in GWP calculations. Baseline radiative forcing is derived
from the RCP scenario database.
Temperature. Temperature calculations are all based on IPCC AR5 Table 8.SM.11.2. It should be noted that the IPCC equations were designed
for marginal emissions changes; therefore, using this approach to calculate
temperatures resulting from the background RCPs and
the additional emissions pulses introduces a potential uncertainty. In
order to calculate future temperatures, we also account for the present-day
radiative forcing imbalance. Medhaug et al. (2017) suggest that this
imbalance likely lies between 0.75 and 0.93 W m-2. We use the mean (0.84 W m-2) as the central estimate and the range of this estimate in the
sensitivity analysis presented above. The sum of the coefficients of the
equations in the IPCC temperature impulse response functions (1.06) is the
sensitivity of the climate to an additional W m-2; assuming that a
doubling of CO2 yields 3.7 W m-2, then the climate sensitivity
implied by the IPCC suggested coefficients is 3.92. As a sensitivity
analysis, the coefficients were scaled to yield climate sensitivities of 1.5
and 4.5 to mirror the likely range estimated by the IPCC.
Damages. Damages as a percent of GDP were calculated by multiplying
a constant by the square of the temperature change since the baseline period.
For example, D(2050)=a⋅ΔT(2050)2⋅ GDP. The net
present value is then calculated using the discount rate such that NPV(D(t))=D(t)/(1+r)t-2010. Hsiang et al. (2017) present a recent justification
for using a quadratic function for damages. For the sensitivity analysis,
damage exponents of 1.5 or 3 were considered. Other formulations of the
damage function have been considered in the literature. The first alternative
is explicit calculation of damages within integrated assessment models.
Another alternative is to include a higher-power term in addition to the
square exponent so that at low temperatures damages rise quadratically, but
at high temperatures damages accelerate (Weitzman, 2010). Finally, some
analyses account for the impact of climate change on the economic growth
rate, finding substantially higher damages (Dell et al., 2012; Moore and
Diaz, 2015). The damage constant (a) (which cancels out in this particular
application) and the GDP pathway are taken from the Nordhaus DICE model
(Nordhaus, 2017). Sensitivity analyses used a growth of 0.5 and 1.5 times
that of the baseline growth for each 5-year time period in the Nordhaus
scenario. The GDP growth rates over the 21st century from DICE (2.5 %)
and the high and low growth rate scenarios (1.3 % and 3.8 %) are
consistent with the estimate of 21st century per capita GDP growth from
Christensen et al. (2018) of 2.1 % (with a standard deviation of
1.1 %), when added to the population growth rate of 0.4 % from DICE
(see the Supplement for a graph of the GDP scenarios). A temperature offset
was also used because it is not clear what baseline temperature should be
used for the damage function. A central value of 0.6 ∘C (the
temperature change from 1951–1980 compared to 2011 based on the NASA
GISSTemp surface temperature record; GISTEMP, 2017) is used, with
sensitivities of 0 ∘C as a lower bound and 0.8 ∘C (the
temperature change from 1880 to 2012 from the 2014 National Climate
Assessment) as an upper bound. For the RCP3PD scenario, some future years
(fewer than 1 out of 1000 of the total years considered across all
sensitivities and generally only for years near the end of the analysis) are
cooler than the baseline temperature; in those years the net temperature
change is set to zero to avoid numerical problems.
Discounting. Discount rates at 0.1 % intervals between
0.5 % and 15 % were used in the analysis.
Equivalent GWP timescale. The above calculations produce
net present damages resulting from a pulse of CH4 and for a pulse
of the same mass CO2. The ratio of these two values is a measure of
the relative impact of CH4 and CO2. This measure of
relative impact can be used to calculate the equivalent GWP timescale that
would produce the same ratio.
Results
Evaluating the climate effects of an emission pulse of <inline-formula><mml:math id="M46" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
Impacts of emission pulses of CH4 and CO2.
Radiative forcing (a), temperature (b), damages (c), and discounted damages
(3 %, a) for an emission pulse of 28.3 MT CH4 (10 ppb in the
first year) and 24.8 times as much CO2 emissions by mass. The
underlying scenario is RCP6.0, with other parameters at their central values.
![]()
The analysis starts by calculating the climate effects of an emission pulse
of CH4. We introduce an emission pulse of 28.3 MT in 2011 (yielding a 10 ppb increase in CH4 concentration in the initial year) applied on top of the GHG
concentrations of Representative Concentration Pathway (RCP) 6.0 (Myhre et
al., 2013). Figure 1 shows the changes in radiative forcing (RF; a),
temperature (T; b), damages (c), and damages discounted at a 3 % rate (d)
out to the year 2300 resulting from such a pulse. Figure 1 relies on
calculations that use central estimates of the uncertain parameters, as
discussed in the Methods section. While the graph is truncated at 2300, the
calculations used in this paper extend to 2500. The impacts of an emission
pulse of CO2 are also shown using 24.8 times the mass of the
CH4 pulse (this factor is chosen to create equivalent integrated
damages over the full time period when discounted at 3 % as shown in Fig. 1d). Figure 1a and b demonstrate the trade-offs between near-term and long-term
impacts when assigning equivalency to emission pulses of different lifetimes.
After 100 years, the radiative forcing effects of the CH4 pulse
decay to 0.04 % of the initial forcing in the year of the emission pulse,
and the temperature effects decay to 4 % of the peak temperature (reached
10 years after the pulse). In contrast, after 100 years the radiative forcing
effects of the CO2 pulse decay to 22 % of the initial forcing,
and the temperature effects decay to 51 % of the CO2 peak
temperature (reached 18 years after the pulse). The immediacy of the
temperature effects for the CH4 pulse creates larger damages in
both overall and discounted dollar terms for the first 42 years. After
43 years, the sustained CO2 effects overtake the CH4
effects. With a different discount rate, a different factor would have been
used to calculate the CO2 mass used for the CO2 pulse,
which would change the crossing point for damages – a higher discount rate
would require a larger CO2 equivalent pulse relative to the
CH4 pulse and therefore an earlier crossing point (and vice
versa). Figure 1c demonstrates the dramatic increase in damage over time due to
the relationship of damage to economic growth. In the case of CH4,
damage peaks in 2032 and declines until 2080 as a result of the short
lifetime of the gas. The increase in damages after 2080 is due to the
component of the temperature response function that includes a 409-year
timescale decay rate such that after 100 years the decrease in the ΔT2 component of the damage equation is about 0.5 % year-1, and
because that decay rate is slower than the rate of GDP growth, net damages
grow. Figure 1d demonstrates the dramatic decrease in future damages when
applying a constant discount rate. Taken as a whole, these four figures
demonstrate the trade-offs required when attempting to create equivalences for
emissions of gases with very different lifetimes.
Implying a discount rate
This analysis of evaluating the radiative forcing, temperature, damages, and
discounted damages of a pulse emission can be used to calculate the
consistent GWP timescale for a given discount rate or, conversely, the
discount rates that are consistent with a given GWP timescale by comparing
the net present discounted marginal damages of CH4 to
CO2. Figure 2 shows the relationship between the discount rate and
the GWP timescale. Here we focus on what discount rates are consistent with a
GWP time horizon in order to show the discount rates implied by common
choices of GWP timescales. The converse calculation is relevant for an
audience that has a preferred discount rate and is interested in the implied
GWP timescale.
GWP timescales consistent with discount rates based on consistency
of the GWP ratio with the ratio of net present damages of CH4 and
CO2, including the interquartile and interdecile bands and maximum
and minimum values based on a sensitivity analysis.
![]()
From Fig. 2, the discount rate implied by the GWP100 is 3.3 %
(interquartile range of 2.7 % to 4.1 %). The discount rate implied by
a 20-year GWP timescale is 12.6 % (interquartile range of 11.1 % to
14.6 %). The results in the figure are truncated to the year 2300 and the
calculation is truncated to the year 2500, which may matter at very low
discount rates due to the long lifetime of CO2. At a 3 %
discount rate, 90 % of the discounted CO2 damages from an
emissions pulse comes in the first 157 years and 95 % in 189 years. For
CH4, the equivalent of 90 and 95 % is
87 and 123 years, with the long tail on
temperature effects causing elongated damages beyond the lifetime of the gas
itself. Even at a 2 % discount rate, 95 % of the CO2
damages come in the first 287 years. At discount rates lower than 2 %,
however, truncation effects can account for errors in damage ratio estimates
of greater than a percent, indicating that longer calculation timeframes may
be necessary to capture the full effect of the emissions pulse.
There is much discussion regarding which discount rates are most appropriate
for use in evaluating climate damages. Since 2003, the US government has used
discount rates of 3 % and 7 % to evaluate regulatory actions, and
3 % was deemed appropriate for regulation that “primarily and directly
affects private consumption” and 7 % for regulations that “alter the
use of capital in the private sector” (OMB, 2003). From the current
analysis, a 3 % discount rate is consistent with a GWP of 118 years
(interquartile range of 84–171 years) and 7 % with a GWP of 38 years
(interquartile range of 32–47 years). The OMB Circular also recognizes that
there are special ethical considerations when impacts may accrue to future
generations, and climate change is a prime example of an impact for which
discount rates lower than 3 % could be justified. A number of researchers
have advocated for time-dependent declining discount rates (Weitzman, 2001;
Newell and Pizer, 2003; Gollier et al., 2008). The UK and France both already
use declining discount rates in policy-making, and in both cases, the
certainty equivalent discount rate drops below 3 % within
100 years and approaches 2 % within 300 years (Cropper et al.,
2014).
This paper does not select a single “correct” discount rate. However,
the analysis shows that the 100-year timescale is consistent, within the
interquartile range, with the 3 % discount rate that is commonly used for
climate change analysis. In contrast, a 20-year time horizon for the GWP
implies discount rates larger than those used in any climate change analysis
publications to date.
Sensitivity analyses
Figure 2 shows the median, interquartile, interdecile, and extremes of the
equivalent GWP time horizon corresponding to a given discount rate from a
sensitivity analysis. The uncertainty was calculated assuming equal
likelihood of each of the 972 combinations of all of the parameter choices
used in this paper: four RCPs, three climate sensitivities, three damage exponents,
three forcing imbalance options, three temperature offsets, and three GDP growth rates.
The ranges chosen for each parameter are described in the Methods section. The
parameters with the largest effect on the uncertainty of the calculated GWP
(at a discount rate of 3 %) are the rate of GDP growth and the damage
exponent (see Table 1). For these six parameters, the choices that lead to
larger damages from CH4 relative to CO2 are a low GDP
growth, a low damage exponent, a low-emissions scenario, a higher temperature
offset (e.g., assuming that damages are a function of warming from
preindustrial, not warming from present day), a lower climate sensitivity,
and a higher current forcing imbalance. The general trend is that the more
that damages are expected to grow in the future (e.g., high GDP growth,
damage exponent, or emissions scenario), the longer the equivalent timescale
is for a given discount rate.
Parameter sensitivity analysis: examining the sensitivity of the
GWP–discount rate equivalency as shown in the uncertainty ranges in Fig. 2 as
a function of the individual parameters of the calculation. The ratio is
calculated as the ratio of the median of the estimated GWPs given the highest
and lowest value of each parameter. The results in this table are derived
assuming a discount rate of 3 %.
Parameter
Ratio of
highest to lowest
damages estimate
GDP
2.07
Damage exponent
1.63
Scenario
1.31
Temperature offset
1.26
Climate sensitivity
1.16
Forcing imbalance
1.02
Optimal timescale of non-CO2 gases. Implicit timescale
evaluated for non-CO2 gases with the GWP to damage ratio for the
two most common GWP timescales. Asterisks indicate no exact match between GWP
ratio and damage ratio; the closest value is given instead. The third and fourth
columns show the ratio of the GWP for a given gas to the calculated damage
ratio. Interquartile uncertainty ranges are presented for the timescale and
damage ratios for CH4. The results in this table are derived assuming a
discount rate of 3 %.
Gas
Lifetime
Optimal
GWP100 / damage
GWP20 / damage
timescale
ratio
ratio
CH4
12.4
120 (84–172)
1.15 (1.52–0.87)
3.4 (4.49–2.57)
N2O
121
*52
0.85
0.84
HFC-134a
13.4
115
1.11
3.2
HFC-23
222
*105
0.71
0.62
PFC-14
50 000
>400
0.62
0.45
While CO2 and CH4 are the largest contributors to climate
change (as evaluated by contributions of historical emissions to present-day
radiative forcing as in Table 8.SM.6 in the IPCC and by the magnitude of
present-day emissions as evaluated by the standard GWP100), it is also
informative to evaluate emissions of other gases with these techniques.
Table 2 shows five gases and their atmospheric lifetimes. For each gas, an
“optimal” GWP timescale was calculated that would replicate the ratio of
net present damage of that gas to CO2 at a discount rate of
3 %. The ratio of the GWP100 and the GWP20 to that optimal
damage ratio is also shown. For longer-lived gases (e.g., N2O and
HFC-23), there is no integration time period that can produce a ratio as
large as the calculated damage ratio at a discount rate of 3 %. For these
gases, we list the timescale that yields the maximum possible ratio and note
that the GWP for longer-lived gases is fairly insensitive to timescale
(further comparisons of non-CO2 gases are presented in the Supplement).
This table shows that at a discount rate of 3 % and as evaluated using
net present damage ratios, the use of a 100-year timescale is consistent
(interquartile range) with the optimal timescale / damage ratios for methane.
For gases with lifetimes in centuries, the GWP at any timescale undervalues
these gases, but the magnitude of that undervaluation is somewhat insensitive
to the choice of timescale. For the longest-lived gases, the GWP also
undervalues reductions in these gases, but the longer the timescale the
better the match.
In addition to investigating the sensitivity of these results to different
choices of the six listed parameters and five different gases, several
other sensitivity experiments were performed. These experiments were chosen
to investigate whether certain assumptions are important and
alternate approaches to constructing the model.
The first set of experiments involve analysis choices that end up having
little difference in terms of timescale estimation. In general, this is
because changes in these choices affect both the GWP and the damage
estimation equally and therefore cancel out. One experiment involved
changing the size of the emissions pulse to 373 MMT (about 1 year of
anthropogenic emissions according to Saunois et al., 2016). The effect on
damage ratios of this change was less than 1 %. Another experiment
involved doubling the radiative efficiency of methane; while this led to a
doubling of the estimated damage ratio, it also led to a doubling of the
estimated GWP such that the change in estimated timescale was about
1/10 of 1 %. This experiment confirms that timescale estimates are
insensitive to updates to estimates of the radiative efficiency of individual
gases (such as the finding of Etminan et al., 2016, that methane has greater
forcing effects than previously estimated). A third experiment arose because
of the question of consistency between the treatment of CO2 and
CH4 in terms of climate–carbon feedbacks (Gasser et al., 2017;
Sterner and Johansson, 2017). Using the CO2 lifetime from Gasser et al. (2017) without climate–carbon feedbacks, an increase in damage ratios of
about 8 % was estimated, but a similar increase in GWP of about 7 %
was estimated, with a net effect on timescales of less than 1 %. The
converse experiment (including climate–carbon feedbacks in both the
CO2 and CH4 lifetimes) was not analyzed due to the
increased complexity of the calculation. However, given that the virtue of
the GWP is its simplicity, the authors suggest that the use of lifetimes
without climate–carbon feedbacks for either gas should be preferred over the
inclusion of those feedbacks in the lifetimes of both gases (Sarofim, 2016).
Another experiment considered the use of a Ramsey-type framework for
discounting future damages. The use of such a framework has been recommended
by the National Academies (NAS, 2017). In this framework, discount rates are
a function of the marginal utility of consumption, the pure rate of time
preference, and the future growth rate of per capita consumption. It is the
latter dependence that makes this sensitivity analysis particularly
interesting, as this pairs higher consumption growth (leading to higher
damage ratios) with higher discount rates (leading to lower damage ratios).
For this experiment, the Ramsey parameters were calibrated to yield an
average discount rate for the reference GDP of 5 % over the first
30 years of the analysis given a pure rate of time preference of 0.01 %.
Under this assumption, the median timescale under the reference GDP scenario
increases to 135 years because even though the initial discount rates are
higher than 3 %, over the entire period of the analysis the average
discount rate is only 1.5 %. However, unlike in the original analysis,
under the high GDP growth scenario the damage ratio increases and the
equivalent timescale decreases to 90 years because the increase in discount
rate resulting from high growth has a larger effect on damages than the
long-term increase in GDP (and vice versa for low GDP growth). The difference
between the damage ratios for the high and low GDP growth scenarios is still
about a factor of 2. A future analysis could pair GDP scenarios with
emissions scenarios to take into account the potential correlation of the
two.
Boucher (2012) and Fuglestvedt et al. (2003) both applied similar approaches
to the one used in this paper, but both papers identified a discount rate
consistent with the GWP100 that was somewhat lower than the median 3.3 %
value found in this paper. The most evident difference between the approach in
these previous papers and this article is that this article assumes that
damages are expressed as a percent of GDP, and the previous analyses did not.
In order to more closely emulate the Boucher and Fuglestvedt approach, the
model was tested by using constant GDP over the entire time period, and the
GWP100 was found to be the most consistent with a discount rate of 1.2 %
(interquartile range of 1.0 % to 1.9 %) in contrast to 3.3 %
(interquartile range of 2.7 % to 4.1 %).
Myhre et al. (2013) justified the exclusion of the 500-year GWP based on the
large uncertainties and ambiguities involved with far future projections.
This analysis extends through 2500 and therefore might be subject to some of
those same uncertainties. Therefore, the effect of two shorter time periods
was investigated. When truncating the analysis after 150 years, the GWP100
was still found to be consistent with a discount rate of 3.3 %, with the
upper interquartile bound also remaining constant at 4.1 %, though the
lower end of the interquartile range decreased modestly to 2.4 %. When
the analysis was truncated at 100 years into the future, the implicit
discount rates dropped more substantially, to 2.6 % (interquartile range
of 1.5 % to 3.5 %). Truncating the analysis will naturally make
CH4 mitigation appear more favorable relative to CO2,
but even discount rates as small as 3 % are sufficient to make effects
more than 150 years into the future inconsequential to the results.
A final experiment considered the inclusion of damages due to rate of change
and due to absolute temperature. The inclusion of rate-of-change damages
has had important influences on previous analyses. For example, in Manne and
Richels (2001), the dynamic optimization solution for approaching a
temperature threshold placed little value on CH4 reduction relative
to CO2 until a couple decades before the threshold was reached; but
when a rate-of-change requirement was added, the relative value of
CH4 reduction stayed fairly constant over the time period. The
challenge for this analysis is in determining the appropriate damage form, as
the literature for estimating damages due to rate of change is not as robust
as for absolute changes. As a test case, the peak rate-of-change damages
under the median parameter values were calibrated to be equal to the absolute
damages in the year 2060 (50 years into the analysis). The effect of
the inclusion of this effect was to increase the damage ratio of CH4 to
CO2 by 2.4 %. This fairly modest impact is consistent with
the results of Bowerman et al. (2013) and Rogelj et al. (2015), which suggest that
near-term mitigation of SLCFs has modest effects on reducing the peak rate
of change for higher future emissions scenarios and that delayed SLCF
mitigation may yield most of the same benefits as immediate SLCF mitigation
in terms of both peak absolute change and rate of change. In order
examine how this effect could be sensitive to a lower emissions scenario, the
analysis was repeated for the RCP3PD scenario by itself. Under this
assumption, the damage ratio increases by 53 %, resulting in a decrease
in the optimal timescale for RCP3PD associated with a discount rate of
3 % from 94 to 54 years. This result is also consistent with
Bowerman et al., who found more benefit in reducing near-term SLCF emissions
if future emissions are expected to be low.
Additional uncertainties
There are a number of uncertainties involved in this analysis. They can be
divided into three categories: those that may change the relative
climate-related discounted damages of CH4 compared to CO2
but have minimal effect on the implied timescale of the GWP, those that have
a large impact on the implied timescale, and those effects of CH4
and CO2 that are unrelated to their climate forcing.
As shown above, uncertainties in this analysis that do not have a large
impact on the calculated GWP timescale include factors that have similar
effects on the GWP and the CH4 : CO2 discounted damage
ratio, such as radiative efficiency and consistent treatment of climate–carbon
feedbacks.
In contrast, the timescale of ocean heat uptake, the lag between the timing
of atmospheric temperature response to forcing and the response of sea level
(e.g., Zickfeld et al., 2017), and other issues that are inherent to the
timing of climate impacts – but are not necessarily included in the GWP
calculation – might all affect the implied timescale. One potential way to
explore some of these effects would be to use a more complex climate model to
evaluate the radiative forcing and temperature effects of the emission
pulses. The shape of the damage function can also have a substantial effect;
different exponents for the polynomial form were tested, as was the inclusion
of rate of change, but the full range of possible damage functions is
substantially larger, including multi-polynomial behavior (Weitzman, 2001)
and the potential for persistent influences on economic growth (Burke et al.,
2015).
An additional category of effects has less relevance to an analysis of
an appropriate timescale for climate impacts, but would be important for overall
valuation. These are generally gas-specific effects that should most
appropriately be considered on a case-by-case basis rather than folding into
a timescale analysis that will influence the mitigation choices for all
gases. One example is the inclusion of CO2 fertilization effects,
which would reduce the relative importance of decreasing CO2
compared to other gases. Other examples include the health effects of
O3 produced by reaction of CH4 in the atmosphere (Shindell et al.,
2015; Sarofim et al., 2017), CO2 effects on ocean acidification,
and the possible reduced efficacy of CH4 compared to CO2
(Modak et al., 2018). These effects can be important for making mitigation
decisions but are outside of the scope of consideration for a study
focusing on how to choose a time horizon for comparing climate impacts. As an
example, if the solution to undervaluing CH4 mitigation due to its
O3 effects is to reduce the appropriate timescale for GHG comparisons,
an identical gas without O3 chemistry implications would be similarly
prioritized. One potential approach that could be explored might be to apply
a multiplier to the GWP after calculation to take into account these
non-climatic effects, much like the GWP of methane takes into account
indirect effects on climate through the production of tropospheric
O3 and stratospheric H2O by the use of a multiplicative factor.
Caveats
The analysis presented here suggests that the use of a 100-year time horizon
for the GWP is in good agreement with what many consider an appropriate
discount rate; however, we offer several caveats. Most importantly, this
analysis makes the assumption that the net present damage of CH4
and CO2 is the best metric for evaluating the relative impact of gases.
When analyzing several different common metrics, Azar and Johansson (2012)
asked whether society would prefer integrated metrics such as the GWP, single
time period metrics such as the GTP, or economic metrics such as the global
damage potential, which is parallel to the metric given primary weight in this
paper. Considering the applications of a metric within the context of an
integrated assessment model could enable the analysis of more complex economic
interactions. Alternatively, a decision-making framework might consider
factors other than damages; for example, in a multistage decision-making
process under uncertainty, it might be possible that long-lived gas
mitigation should be prioritized in order to increase future option value. Or
there might be reasons to prioritize mitigation options that apply to capital
stocks with long lifetimes or to decisions that involve path dependence, as
those decisions would be more costly to reverse in the future.
This metric approach is also not designed to achieve a long-term temperature
goal such as stabilization at 2 ∘C above preindustrial
temperatures. We note that no metric designed to trade off emission pulses is
consistent with stabilization. One solution to this dilemma is the GWP*
introduced by Allen et al. (2016), which creates an equivalence between an
emission pulse of CO2 and a constant stream of CH4. This
analysis only looks at a pulse of emissions in 2011 and does not examine
whether the equivalent timescale might change over time.
Conclusions
This analysis uses a global damage potential approach to calculate the
implicit discount rate corresponding to different GWP timescales. While
this is not the first analysis to calculate the implicit discount rate of the
100-year GWP (Boucher, 2012; Fuglestvedt et al., 2003), the framework
presented here allows for a more complete and wide-ranging analysis of
sensitivities than has been presented previously, and the connection between
the timescale and the implicit discount rate is made more clearly. The 100-year GWP is the inter-gas comparison metric with the widest use, and the
results presented here show that the 100-year timescale is consistent with an
implied discount rate of 3.3 % (interquartile range of 2.7 % to
4.1 %). Alternatively, the 3 % discount rate used for calculating
social damages in some regulatory impact analysis contexts is consistent with
timescales of 84–171 years. The uncertainty range in the results is the most
sensitive to assumptions regarding future GDP growth and to the choice of
exponent in the damage function. These results are insensitive to assumptions
regarding radiative efficiency, pulse size, and consistent treatment of
climate–carbon feedbacks. At discount rates of 3 % or higher, the
analysis can be truncated to 150 years (rather than the default calculation
through 2500) with little effect. The inclusion of damages resulting from the
rate of change in addition to absolute temperature changes has little effect
except in the case of a low-emissions future, for which it results in a decrease
in the timescale consistent with a 3 % discount rate to 54 years.
Applying the methodology in this paper to calculate the implied intertemporal
values of a 20-year GWP, a timescale that has received some recent attention,
results in an implicit discount rate of 12.6 % (interquartile range of
11.1 % to 14.6 %).
These results provide support for the contention that 100 years is a
reasonable timescale choice for the GWP given the assumption that the
relative climate damage of pulses of different greenhouse gases is an
appropriate means of valuation and that the 3 % discount rate is a
reasonable measure of the value of the future. This finding is robust to a
number of sensitivity analyses. In contrast, the analysis suggests that the
20-year GWP timescale is the most consistent with an implicit discount rate much
higher than the standard social discount rate, except in scenarios with low
future emissions and high rate-of-change damages, similar to concerns
expressed in other analyses (Shoemaker and Schrag, 2013). However, while the
implicit timescale was derived from analyzing the climate impacts resulting
from CH4 emissions relative to CO2 climate impacts, the
results do not necessarily inform a specific relative importance of
CH4 mitigation compared to CO2. Such a relative
importance calculation should take into account the latest research on
radiative efficiencies (Etminan et al., 2016) and could potentially also
take into account non-climate impacts like the health effects of
CH4-derived O3 (Shindell, 2015; Sarofim et al., 2017).
The inclusion of non-climate impacts could perhaps use an adjustment factor in
the same way that the CH4 GWP already includes adjustment factors
for the climate effects of CH4-derived O3. Additionally,
the appropriate GWP timescales can also be informed by the manner in which
the metric is being used for policy or informational purposes.
The methodology presented here is transparent (the code is available in the
Supplement), rigorous (the parameters and functional forms are derived from
respected sources), and flexible (as demonstrated by a wide range of
sensitivity analyses from the inclusion of rate-of-change damages to Ramsey
discounting). This framework can be a valuable resource for quantitatively
examining appropriate timescales given different assumptions about
discounting, the relationship of damages to both absolute and rate of
temperature changes, tipping points, future emissions scenarios, and other
factors.